Question

Currency options. What are the two types, and what is the difference between them? What is the break-even point for each type? Conceptually understand and be able to mathematically work with them.

A. You purchase a put option on the Canadian dollar with a strike price of $0.91 and a premium of $0.02. If before expiration the spot rate of the Canadian dollar is $0.92, will you exercise the option?

b. What if the spot rate before expiration is $0.88?

c. What is the break-even spot rate?

d. If a firm bought this option to hedge a C$100,000 receivable and exercised it when the spot rate is $0.875, how many U.S. dollars would the firm receive?

Answer 1

The two types of options (and not just currency options) are the call and put option. In a call option, the buyer of the option obtains the right but not the obligation to purchase the underlying asset (which is a currency in case of currency options) at a fixed price known as the option's strike price irrespective of the actual price of the asset. In case of a put option, the buyer of the option obtains the right but not the obligation to sell the underlying asset at the option's strike price irrespective of the actual price of the asset. Both options come with a fixed tenure and can be either exercised prior to expiry or at expiry (American Options. A European Option can be exercised only when its tenure is over).

Call Option:

Let the option's strike price be K1, Premium be C and Underlying Asset Price be S1. Then at expiry break-even will occur when:

S1 - K1 = C where S1 - K1 is the call payoff and S1 > K1. By buying the underlying asset at K1 instead of the higher market price of S1, the option buyer makes a profit of S1-K1 which should equal the option premium (price paid for buying the option) C for the buyer to break-even.

Put Option:

Let the option's strike price be K2, Premium be P and Underlying Asset Price be S2. Then at expiry break-even will occur when:

K2 - S2 = P where K2 - S2 is the call payoff and K2 > S2. By selling the underlying asset at K2 instead of the lower market price of S2, the option buyer makes a profit of K2 - S2 which should equal the option premium P for the buyer to break-even.

(a) Strike Price of Put Option = K2 = $ 0.91 and Premium Paid = P = $ 0.02. Underlying Asset Price (Canadian Dollar Price) = S2 = $ 0.92

As S2 is not lesser than K2, the put option is not profitable to exercise. Hence, the same will not be exercised.

(b) If S2 = $ 0.88, then K2 > S2 and exercising the option will generate a profit. Hence, the same will be exercised.

(c) Let the break-even exercise price be S2. By the break-even condition described earlier, we have:

K2 - S2 = P

0.91 - S2 = 0.02

S2 = 0.91 - 0.02 = $ 0.89

(d) Receivable = C $ 100000, Spot Price = $ 0.875 and Strike Price = $ 0.91

If the put option is exercised, then the number of US $ received = 100000 x 0.91 = $ 91000